Stock assessment for fishery management - Library

144 Stock assessment for fishery managementcould be caused by unusual conditions at that time or by measurement errors in theabundance index, catch data, recruitment index, or even the mean weight. If conditionswere anomalous that year (e.g. unusual sea temperature), then the point should beexcluded from analysis.If the abundance index is likely to be at fault, perhaps due to a very small effortand consequently a small sample on which to calculate CPUE, or due to an unusualdistribution of effort in space or time, then it is again reasonable to exclude the point.If the problem is due to sample size, another approach might be to try to obtain anestimate of variance for each abundance index, and use the weighted least squares fit;the point based on the small sample would then automatically be down-weighted.Other possible reasons for outliers and what to do about them are discussed in the helpfiles. It is re-emphasized that data points should never be omitted from the analysisunless there is a good reason to do so.The CEDA help files also describe how to deal with “influential points”, that is,points whose presence or absence in the data set makes a large difference to the resultsobtained. An influential point is not (necessarily) the same thing as an outlier.Influential points tend usually, but not invariably, to lie near the extremes of the dataset, i.e. near the lowest and the highest stock sizes, where they exert a strong pull on thefitted models. Potential influential points can often be identified from plots of residualsagainst expected catches: they will be the ones corresponding to isolated large or smallexpected catches, usually with small residuals. If a point is suspected as influential, itcan easily be checked by toggling it out and seeing if the parameter estimates changesubstantially.The data for an influential point should be carefully scrutinized, just as for apotential outlier. If there are serious data problems, then the point should be droppedfrom subsequent analysis. If not, then sensitivity analysis should be used to determinethe effects of including or excluding the point. It is definitely wrong to exclude aninfluential point and then forget about it, as one might for an outlier; the results willthen be biased and the precision of the estimates reduced.8.2.5 Model diagnostics – using the “goodness-of-fit”Numerical measures of goodness of fit (GoF), such as the well-known coefficientof determination, R-squared, are often quoted as evidence of how well a model fits.This is only meaningful for data that accord with the model assumptions, i.e. wherethe residual plots show no trends or patterns. The R-squared statistic is calculated byCEDA but should only be used in comparing fits that both use the same error model.Each error model has a corresponding GoF defined in a distinct way. Therefore, it isnot possible to use GoFs to compare fits based on different error models; these shouldbe done with residual plots alone. Under a fixed error model, there are two allowabletypes of comparison: between different model assumptions when fitting the same data,or between the same model assumptions when fitting “similar” data. Some types ofdata comparison are more reliable than others, and three examples are given below:1. The best type of comparison is between different sets of catch or recruitmentindex data with the same number of points, used to fit the same abundance data.This will not be a very common event, as different catch series should only occurif some values are missing and have been filled in by more than one method.2. It is also reasonable, but less statistically sound, to use R-squared when comparingfits using different series of abundance indices, again of the same length and withmissing values, if any, at the same points. The comparisons should not be takentoo literally. Graphs of observed and expected values of different abundanceindices can often reveal more useful information.3. It is not reasonable to use R-squared to compare two series of different lengths,or with missing data and/or points deliberately excluded in different places.